September 21, 2017 10:37am EDTSeptember 21, 2017 10:37am EDTRun expectancy is an analytics stepping stone, and now that it's creeping into MLB broadcasts more, it's important to understand just where it comes from.

Editor's note: This is the fourth installment in a Sporting News series that looks to bridge the gap of understanding between adherents of traditional baseball statistics and new-school analytics.

Up until this point in Stat to the Future, we've discussed tools for evaluating players: Using wOBA to evaluate hitters instead of BA, using FIP to evaluate pitchers instead of ERA and so forth. But baseball is so much more than throwing baseball players onto a field and expecting them to win a game by themselves.

We’ll look at a practical application of sabermetrics, and a tool that is the foundation for a lot of advanced stats: run expectancy.

What is run expectancy?

Let’s say that a player comes up to bat with runners on second and third and one out. Run expectancy (RE) answers the question “how many runs could his team expect to score from this situation?

RE tells us how a team could expect to fare in any situation, and what outcomes of a given plate appearance are favorable or unfavorable towards scoring runs in the inning.

In baseball, there are 24 possible “base states” for which we can calculate RE — there are eight different possible configurations of baserunners (ranging from bases empty to bases loaded) and three different out states (no outs, one out, two out). So, some possible base states include two outs and no one on base, no outs and bases loaded, one out and a runner on third, and so on. RE tells us in a given situation, how many runs one could expect to score from that base state until the end of the inning.

We’ll return to the above example, of a runner on second and third, with one out. RE tells us that from that situation, teams will score 1.376 runs on average (obviously, a team can’t score .376 runs — this is an average). In a different situation, the RE changes — so if there are two outs and nobody on, a team’s RE differs from if there was nobody out (0.098 compared to 0.481).

RE only tells us how many runs one would expect to score in an inning from a given base state until the end of the inning. It doesn’t care what runs came before it. So if the batter leading off an inning hit a solo shot, the run expectancy for the next plate appearance is the same, because RE only measures how many runs should be scored from that plate appearance until the end of the inning.

How is RE calculated?

RE’s calculation is straightforward. Take a historical sample size (all the numbers used in this article are based on RE figures from 2010-2015), and then look at every plate appearance over that time span. Each plate appearance can be classified according to its base state, so group together all plate appearances by base state.

Then, within those groups, sum up all the runs that scored from a given plate appearance until the end of the inning, and then divide by the total number of plate appearances in that group to find the RE for that base state.

Notice that for RE, you must choose a historical sample size because the league-wide offense has changed dramatically since stats were first kept on baseball, one cannot simply look at RE since stats were first kept on baseball. The run expectancy for 1901-1919 shouldn’t be used in 2017 because league-wide offensive numbers have jumped up significantly since the deadball era.

Similarly, it is also wise to adjust for park factors in determining RE. Since Coors Field produces higher scoring games than AT&T Park, it would be slightly inaccurate to use a single RE matrix for both parks.

Why should I care about RE?

Glad you asked.

Run expectancy at its core can help tell managers what move to make. Let’s say that there are runners on second and third and one out. To minimize the number of runs scored in the inning, should a manager have the batter at the plate intentionally walked to set up a double play?

To determine whether this is a good idea, we look at the initial RE, then look at what the RE would be after the IBB.

Using league-wide data from 2010-2015, with runners on second and third and one out, RE is 1.376, but with the bases loaded and one out, RE jumps up to 1.541. In general, this would be a bad idea, because the expected number of runs to score in the inning increases.

This is where adjustments based on the situation should be made. If we have an average hitter at the plate, our RE is 1.376, but if there’s a pitcher batting behind them, then with an IBB, the RE instead drops to .879. So in this instance, it is wise to IBB the hitter to load the bases.

Managers can judge their decisions by looking at whether it raises or lowers the RE. Generally, if RE is raised, it’s a good idea, but if RE is lowered, then it isn’t. RE matrices can be an extremely valuable in-game management tool if used properly.

RE also has applications outside of individual games. For instance, one can look at a player’s value situationally by looking at their RE24. If a player steps up to the plate and hits a double, it raises the run expectancy in the inning. If a player grounds out instead, it lowers the run expectancy. RE24 is the sum of all those rises and falls, plus any runs that scored because of the player’s plate appearance. RE24 is a useful stat for those looking for an alternative to RBI.

The biggest application of RE, however, is in the calculation of wOBA. When I discussed wOBA as an alternative to BA, I mentioned that plate outcomes like home runs and singles are weighted differently, based on the value they provide. That value is calculated using RE: to determine the value of a single, we can look at every single in the league within a given time frame, and see how it raised or lowered the run expectancy, then divide that by the total number of singles in the league. We can do this for every plate outcome (single, double, triple, home run, walk, hit by pitch, out), then scale the numbers to make sense in terms of wOBA.

RE is fundamental to sabermetrics and our modern understanding of baseball. It’s a building block of sorts for learning sabermetrics and extremely useful, but beware: I’m not responsible for any blown gaskets the next time the manager of your favorite team makes the best hitter in the lineup bunt.